How to make a 120 degree angle without a protractor

Written by david robinson| 13/05/2017

A compass can be used for more than just drawing circles. (John Foxx/Stockbyte/Getty Images)

Being able to draw angles without the aid of a protractor is an important architectural and mathematical skill. Many angles can be drawn with a compass, also known as a pair of compasses. A compass is a drawing tool with two pivoting legs, one ending in a spike and the other ending in a pencil point. The ratio of the circumference of a circle to its diameter is very close to 3:1, and because 120 degrees is a third of a full circle, a pair of compasses can be used to draw a 120-degree angle.

Mark a dot on a sheet of paper. Draw a circle using a compass and a sharp pencil, using the dot as the centre point. Take care not to alter the compass setting when the circle is complete.

Place a ruler over the circle with the edge passing through the centre of the circle and any point on the perimeter of the circle. Make a clear mark where the ruler crosses the circumference.

Ensure that the radius of the compass has not changed, and then place the pivot point on the mark where the straight line crossed the circle perimeter. Draw a new circle.

Draw straight lines from the centre of the first circle to the two points where the second circle crosses the perimeter of the first circle. This creates the points of two equilateral triangles, with internal angles of 60 degrees. The angle between these two lines is 120 degrees.

Tip

Many different angles can be drawn using a compass and a ruler, including those measuring 30, 45, 60, 90 and 180 degrees.

Warning

The radius of the compass must remain unchanged throughout the process. If it changes, reset it to the original value.

Tips and warnings

Many different angles can be drawn using a compass and a ruler, including those measuring 30, 45, 60, 90 and 180 degrees.

The radius of the compass must remain unchanged throughout the process. If it changes, reset it to the original value.